EXAMPLE: All trees lose their leaves or needles in the fall.
ANSWER: The answer would be false because; pine trees do not lose thier needles in the fall
EXAMPLE: The sum of the sequence 1+2+2^2+...+2^n, where n is a whole number, isalwaysa prime number.
choices are: a) when n=4, the sum is 31 b) when n=7, the sum is 57 c) when n=5, the sum is 63.. and d) there is no counterexample. The conjecture is true.
ANSWER: The answer would be [c] because 63 is not a prime number.
Conjectures: True/False and Counterexamples.
EXAMPLE: All trees lose their leaves or needles in the fall.
ANSWER: The answer would be false because; pine trees do not lose thier needles in the fallEXAMPLE: The sum of the sequence 1+2+2^2+...+2^n, where n is a whole number, is always a prime number.
choices are: a) when n=4, the sum is 31 b) when n=7, the sum is 57 c) when n=5, the sum is 63.. and d) there is no counterexample. The conjecture is true.
ANSWER: The answer would be [c] because 63 is not a prime number.